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Abstract

Exponential smoothing methods offer several tools for forecasting and simulating varying time series patterns, including historical wildfire counts. The Box-Cox transform, ARMA errors, trend and seasonal components (BATS), and the trigonometric BATS model (TBATS) are exponential smoothing techniques capable of modeling complex seasonality, non-integer frequencies, and more. The BATS and TBATS frameworks support short- and intermediate-term forecasting and simulation, while also providing a foundation for model-based time series clustering of wildfire counts. The application in this thesis of the BATS and TBATS models aims to support fire agencies in forecasting and simulating wildfire occurrences across Canada on an increased scale that provides alternative methods for future use. Variable length Markov chains (VLMCs) are an extension of traditional fixed-order Markov chains that can reduce model complexity and improve computational efficiency. To assess the practicality and effectiveness of VLMCs in modeling wildfire causes in Canada, they are evaluated in terms of forecasting on both balanced and unbalanced data. Furthermore, VLMCs are used to model the cluster assignment results on the weekly wildfire count time series data over a range of years. We provide preliminary information on clustering weekly wildfire counts using a model-based approach built from TBATS models that can help identify broad characteristics for an upcoming fire season through extensions of Markov chains.